Statistical properties of particles in heterogeneous gas-solid flow were numerically investigated based on the results of a three-dimensional large-scale direct numerical simulation (DNS). Strong scale-dependence and local non-equilibrium of these properties, especially the particle fluctuating velocity (PFV) or granular temperature, were observed to be related to the effect of meso-scale structures formed by the compromise in competition between fluid and particle dominated mechanisms. To quantify such effects, the heterogeneous structures were partitioned into a gas-rich dilute phase and a solid-rich dense phase according to the particle-scale voidage defined through the Voronoi tessellation. Non-equilibrium features, such as the deviation of PFV from Gaussian distribution and anisotropy, were found even in phase-specific properties. A new distribution function for the PFV well characterizing these features was obtained by fitting the DNS results, which takes a typical bi-disperse mode, with phase-specific granular temperatures. The implications of these findings to the kinetic theory of granular flow and traditional continuum models of gas-solid flow were also discussed. (c) 2016 American Institute of Chemical Engineers AIChE J, 63: 3-14, 2017